On the Axisymmeteric Buckling of Thin Spherical Shells

In this work a post-buckling analysis of a thin spherical Shell under the action of uniform external pressure is given. A similar investigation was done by Knightly & Sather (|1|) using a more functional analytic approach. Further in this paper a versal unfolding (see |2|) of the bifurcation equations is carried out. Nevertheless these results have a limited practical importance, as the range of validity is restricted to a small neighborhood of the bifurcation point. This is caused by the fact that the eigenvalues lie closely spaced. Lange & Kriegsmann applied asymptotic integration techniques to overcome these troubles. They obtained results, which are valid at larger distances of the bifurcation point and which give together with the classical bifurcation Solution a nearly total understanding of the complete axisymmetric buckling behavior of the perfect Shell. I will shortly comment on this at the end of the paper.